等价无穷小在求极限中的应用

On the Application of Equivalent Infinitesimal in the Solving of Limit Problems

对于高职高专学生来说,求极限的方法很多样,掌握起来有困难。等价无穷小替换是在求极限中常用的一种方法。但由于对其理解不够深刻,学生常常感到困惑。本文在等价无穷小替换定理的基础上,推广加减运算、复合函数、幂指函数中的等价无穷小替换,使计算极限达到化简为繁、化难为易的目的。

For higher vocational students, there are various kinds of methods to solve limit problems, but they are difficult to mas-ter. Equivalent infinitesimal replacement is a method commonly used in limit operation. But due to the lack of a deep understand-ing, students often get confused. Based on the theorem of equiva-lent infinitesimal replacement, this paper extended to the equiva-lent infinitesimal replacement in addition and subtraction opera-tion, composite function, and exponential function, in order to simplify the calculation of limit.